Showing papers on "Pushdown automaton published in 2004"
13 Jun 2004
TL;DR: This framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures withrespect to pre and post conditions.
Abstract: We propose the class of visibly pushdown languages as embeddings of context-free languages that is rich enough to model program analysis questions and yet is tractable and robust like the class of regular languages. In our definition, the input symbol determines when the pushdown automaton can push or pop, and thus the stack depth at every position. We show that the resulting class Vpl of languages is closed under union, intersection, complementation, renaming, concatenation, and Kleene-*, and problems such as inclusion that are undecidable for context-free languages are Exptime-complete for visibly pushdown automata. Our framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures with respect to pre and post conditions. We demonstrate that the class Vpl is robust by giving two alternative characterizations: a logical characterization using the monadic second order (MSO) theory over words augmented with a binary matching predicate, and a correspondence to regular tree languages. We also consider visibly pushdown languages of infinite words and show that the closure properties, MSO-characterization and the characterization in terms of regular trees carry over. The main difference with respect to the case of finite words turns out to be determinizability: nondeterministic Buchi visibly pushdown automata are strictly more expressive than deterministic Muller visibly pushdown automata.
621 citations
09 May 2004
TL;DR: This paper provides a formal analysis framework of PDA models and introduces the concepts of determinism and stack-determinism, and presents the VP-Static model, which achieves determinism by extracting information about stack activity of the program, and the Dyck model, whose results show that in run-time monitoring, the models slow execution of test programs by 1% to 135%.
Abstract: A key function of a host-based intrusion detection system is to monitor program execution. Models constructed using static analysis have the highly desirable feature that they do not produce false alarms; however, they may still miss attacks. Prior work has shown a trade-off between efficiency and precision. In particular, the more accurate models based upon pushdown automata (PDA) are very inefficient to operate due to non-determinism in stack activity. In this paper, we present techniques for determinizing PDA models. We first provide a formal analysis framework of PDA models and introduce the concepts of determinism and stack-determinism. We then present the VP-Static model, which achieves determinism by extracting information about stack activity of the program, and the Dyck model, which achieves stack-determinism by transforming the program and inserting code to expose program state. Our results show that in run-time monitoring, our models slow execution of our test programs by 1% to 135%. This shows that reasonable efficiency needs not be sacrificed for model precision. We also compare the two models and discover that deterministic PDA are more efficient, although stack-deterministic PDA require less memory.
179 citations
13 Jul 2004
TL;DR: This work considers the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various Probabilistic logics and proves that both qualitative and quantitative model checking for pPDA is decidable.
Abstract: We consider the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various probabilistic logics. We start with properties that can be formulated as instances of a generalized random walk problem. We prove that both qualitative and quantitative model checking for this class of properties and pPDA is decidable. Then, we show that model checking for the qualitative fragment of the logic PCTL and pPDA is also decidable. Moreover, we develop an error-tolerant model checking algorithm for general PCTL and the subclass of stateless pPDA. Finally, we consider the class of properties definable by deterministic Buchi automata, and show that both qualitative and quantitative model checking for pPDA is decidable.
164 citations
27 Sep 2004
TL;DR: A semi-automated verification of a slightly optimised version of Michael and Scott's lock-free FIFO queue implementation is described, and the properties needed to show that the algorithm implements the specification are proved using PVS’s theorem prover.
Abstract: We describe a semi-automated verification of a slightly optimised version of Michael and Scott’s lock-free FIFO queue implementation. We verify the algorithm with a simulation proof consisting of two stages: a forward simulation from an automaton modelling the algorithm to an intermediate automaton, and a backward simulation from the intermediate automaton to an automaton that models the behaviour of a FIFO queue. These automata are encoded in the input language of the PVS proof system, and the properties needed to show that the algorithm implements the specification are proved using PVS’s theorem prover.
116 citations
16 Dec 2004
TL;DR: This paper surveys recent work conducted by the authors together with colleagues on he algorithmic verification of probabilistic procedural programs ([BKS,EKM04,EY04]; a very rich theory emerges for these models.
Abstract: Monolithic finite-state probabilistic programs have been abstractly modeled by finite Markov chains, and the algorithmic verification problems for them have been investigated very extensively. In this paper we survey recent work conducted by the authors together with colleagues on he algorithmic verification of probabilistic procedural programs ([BKS,EKM04,EY04]). Probabilistic procedural programs can more naturally be modeled by recursive Markov chains ([EY04)], or equivalently, probabilistic pushdown automata ([EKM04)]. A very rich theory emerges for these models. While our recent work solves a number of verification problems for these models, many intriguing questions remain open.
111 citations
16 Dec 2004
TL;DR: The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems and it is established that, unlike pushdown games with pushdown winning conditions, visibly push down games are decidable and are 2Exptime-complete.
Abstract: The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptime-complete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptime-complete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined.
86 citations
TL;DR: It is argued that ERP components are indicators of these bifurcations and proposed an ERP-like measure of the parsing model, which can be modeled by a switching of the control parameter in analogy to phase transitions observed in brain dynamics.
Abstract: We describe a part of the stimulus sentences of a German language processing ERP experiment using a context-free grammar and represent dieren t processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter | in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model.
30 citations
TL;DR: A theorem answering the question "how many states does a minimal deterministic finite automaton recognizing the set of base-b numbers divisible by k have?" is presented and proved.
29 citations
20 Dec 2004
TL;DR: The decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ is looked at and applications to automated composition of e-services are identified.
Abstract: Let ${\mathcal M}$ be a class of (possibly nondeterministic) language acceptors with a one-way input tape A system (A; A1, ..., Ar) of automata in ${\mathcal M}$, is composable if for every string w = a1 .. an of symbols accepted by A, there is an assignment of each symbol in w to one of the Ai's such that if wi is the subsequence assigned to Ai, then wi is accepted by Ai For a nonnegative integer k, a k-lookahead delegator for (A; A1, ..., Ar) is a deterministic machine D in ${\mathcal M}$ which, knowing (a) the current states of A, A1, ..., Ar and the accessible “local” information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the k lookahead symbols to the right of the current input symbol being processed, can uniquely determine the Ai to assign the current symbol Moreover, every string w accepted by A is also accepted by D, i.e., the subsequence of string w delegated by D to each Ai is accepted by Ai Thus, k-lookahead delegation is a stronger requirement than composability, since the delegator D must be deterministic A system that is composable may not have a k-delegator for any k We look at the decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ Our results have applications to automated composition of e-services When e-services are modeled by automata whose alphabet represents a set of activities or tasks to be performed (namely, activity automata), automated design is the problem of “delegating” activities of the composite e-service to existing e-services so that each word accepted by the composite e-service can be accepted by those e-services collectively with each accepting a subsequence of the word, under possibly some Presburger constraints on the numbers and types of activities that can be delegated to the different e-services Our results generalize earlier ones (and resolve some open questions) concerning composability of deterministic finite automata as e-services to finite automata that are augmented with unbounded storage (e.g., counters and pushdown stacks) and finite automata with discrete clocks (i.e., discrete timed automata) We look at the decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ Our results have applications to automated composition of e-services E-services provide a general framework for discovery, flexible interoperation, and dynamic composition of distributed and heterogeneous processes on the Internet Automated composition allows a specified composite e-service to be implemented by composing existing e-services When e-services are modeled by automata whose alphabet represents a set of activities or tasks to be performed (namely, activity automata), automated design is the problem of “delegating” activities of the composite e-service to existing e-services so that each word accepted by the composite e-service can be accepted by those e-services collectively with each accepting a subsequence of the word, under possibly some Presburger constraints on the numbers and types of activities that can be delegated to the different e-services Our results generalize earlier ones (and resolve some open questions) concerning composability of deterministic finite automata as e-services to finite automata that are augmented with unbounded storage (e.g., counters and pushdown stacks) and finite automata with discrete clocks (i.e., discrete timed automata).
22 citations
01 Jan 2004
TL;DR: In this paper, the authors explore and compare various conditions on sets of states of which are related to the fact that induced subautomata of accept the whole language L. The methods of several previous works on minimalizations of NFA can be modified so that they fit in their approach.
Abstract: As is well known, each minimal NFA for a regular language L is isomorphic to a subautomaton of the so-called universal automaton for L. We explore and compare various conditions on sets of states of which are related to the fact that induced subautomata of accept the whole language L. The methods of several previous works on minimalizations of NFA can be modified so that they fit in our approach. We also propose a new algorithm which is easy to implement.
21 citations
Patent•
30 Sep 2004TL;DR: A method and apparatus for manipulating a non-deterministic automaton for dynamic verification of a device under test is described in this paper. But this method requires a traversal of the automaton.
Abstract: A method and apparatus for manipulating a non-deterministic automaton (114) and a traversal of a non-deterministic automaton for dynamic verification (112) of a device under test (118).
TL;DR: This work shows Sigma^1_1-completeness of weak bisimilarity for PA (process algebra), and of weak simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets).
Abstract: We show Sigma^1_1-completeness of weak bisimilarity for PA (process algebra), and of weak simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets). We also show Pi^1_1-hardness of weak omega-trace equivalence for the (sub)classes BPA (basic process algebra) and BPP (basic parallel processes).
29 Nov 2004
TL;DR: It is shown that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language.
Abstract: Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.
TL;DR: It is shown that model-checking past pushdown timed automata against Presburger safety properties on discrete clocks and stack word counts is decidable, and the reachability problem for a class of transition systems under some fairness constraints in the form of generalized past formulas is investigated.
13 Dec 2004
TL;DR: An inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input- reversal iterated push down automata.
Abstract: Input-reversal pushdown automata are pushdown automata with the additional power to reverse the unread part of the input. We show that these machines characterize the family of linear context-free indexed languages, and that k + 1 input reversals are better than k for both deterministic and nondeterministic input-reversal pushdown automata, i.e., there are languages which can be recognized by a deterministic input-reversal pushdown automaton with k + 1 input reversals but which cannot be recognized with k input reversals (deterministic or nondeterministic). In passing, input-reversal finite automata are investigated. Moreover, an inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input-reversal iterated pushdown automata. Finally, some computational complexity problems for the investigated language families are considered.
01 Jan 2004
TL;DR: A generic method for deciding semantic equivalences between pushdown automata and finite-state automata, and special attention is devoted to bisimulation-like equivalences (including weak, early, delay, branching, and probabilistic bisimilarity).
Abstract: We propose a generic method for deciding semantic equivalences between pushdown automata and finite-state automata. The abstract part of the method is applicable to every process equivalence which is a right PDA congruence. Practical usability of the method is demonstrated on selected equivalences which are conceptual representatives of the whole spectrum. In particular, special attention is devoted to bisimulation-like equivalences (including weak, early, delay, branching, and probabilistic bisimilarity), and it is also shown how the method applies to simulation-like and trace-like equivalences. The generality does not lead to the loss of efficiency; the algorithms obtained by applying our method are essentially time-optimal and sometimes even polynomial. The list of particular results obtained by our method includes items which are first of their kind.
31 Aug 2004
TL;DR: It is demonstrated that if the number of control states in PDA is bounded by a fixed constant, then the algorithm needs only polynomial time, and probabilistic bisimilarity is decidable over Probabilistic extensions of BPA and BPP processes.
Abstract: We prove that probabilistic bisimilarity is decidable over probabilistic extensions of BPA and BPP processes. For normed subclasses of probabilistic BPA and BPP processes we obtain polynomial-time algorithms. Further, we show that probabilistic bisimilarity between probabilistic pushdown automata and finite-state systems is decidable in exponential time. If the number of control states in PDA is bounded by a fixed constant, then the algorithm needs only polynomial time.
Journal Article•
TL;DR: In this paper, an inherent relation between input-reversal pushdown automata and controlled linear context-free languages is shown, leading to an alternative description of the Khabbaz geometric hierarchy of languages by input reversal iterated pushdown autoencoder automata.
Abstract: Input-reversal pushdown automata are pushdown automata with the additional power to reverse the unread part of the input. We show that these machines characterize the family of linear context-free indexed languages, and that k + 1 input reversals are better than k for both deterministic and nondeterministic input-reversal pushdown automata, i.e., there are languages which can be recognized by a deterministic input-reversal pushdown automaton with k + 1 input reversals but which cannot be recognized with k input reversals (deterministic or nondeterministic). In passing, input-reversal finite automata are investigated. Moreover, an inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input-reversal iterated pushdown automata. Finally, some computational complexity problems for the investigated language families are considered.
Journal Article•
TL;DR: In this article, the authors investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton using Antimirov's derived term of an expression.
Abstract: In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently decorated, the combination of these two algorithms gives the desired result. Reducing the amount of decoration is still the object of ongoing investigation.
28 Jun 2004
TL;DR: The achievements of students on the technical parts of this unit vs. its theoretical parts are compared and the correlation between achievements and two other factors are examined: the students' previous computer-related background (not necessarily computer science) and the level on which they studied mathematics.
Abstract: One of the units in the relatively new high school CS curriculum which is being implemented in Israel is a theoretical unit on computational models. It includes deterministic and non-deterministic finite automata, regular and non-regular languages, closure properties of regular languages, pushdown automata, closure properties of context free languages, Turing machines, the Church-Turing thesis and the halting problem. This paper focuses on part of a study we conducted dealing with the achievements of high school students studying this unit. Specifically, this paper compares the achievements of students on the technical parts of this unit vs. its theoretical parts. We also examine the correlation between achievements of students studying the Computational Models unit, and two other factors: The students' previous computer-related background (not necessarily computer science) and the level on which they studied mathematics.
22 Jul 2004
TL;DR: The design of an algorithm for computing the follow automaton via this structure makes it easier to compare all these small recognizers, and provides a straightforward alternative to the rather sophisticated handling of e-transitions used in the original algorithm.
Abstract: Small nondeterministic recognizers are very useful in practical applications based on regular expression searching. The follow automaton, recently introduced by Ilie and Yu, is such a small recognizer, since it is a quotient of the position automaton. The aim of this paper is to present an efficient computation of this quotient, based on specific properties of the $\mathcal{ZPC}$ of the expression. The motivation is twofold. Since this structure is already a basic tool for computing the position automaton, Antimirov’s automaton and Hromkovic’s automaton, the design of an algorithm for computing the follow automaton via this structure makes it easier to compare all these small recognizers. Secondly such an algorithm provides a straightforward alternative to the rather sophisticated handling of e-transitions used in the original algorithm.
TL;DR: The results imply Σ11-completeness of weak bisimilarity for Petri nets and give a negative answer to the open problem stated by Jancar (CAAP'95): “does the problem of weak BisimilarityForPetri nets belong to Δ11?”
01 Jan 2004
TL;DR: The new algorithm makes use of sorted data in order not to reprocess states that are added or modified as the result of adding the whole set of words, which should make it faster than the Carrasco and Forcada’s algorithm.
Abstract: Finite-state machines are widely used as dictionaries in natural language processing. They offer fast processing time and low memory requirements. We present a new algorithm for adding new words to the language of a cyclic finite-state automaton. The algorithm is an extension to cyclic automata of a semi-incremental Watson’s algorithm for acyclic automata. The conversion is done in the spirit of Carrasco and Foracada’s algorithm for adding new words to cyclic automata. The new algorithm makes use of sorted data in order not to reprocess states that are added or modified as the result of adding the whole set of words. This should make it faster than the Carrasco and Forcada’s algorithm.
05 Apr 2004
TL;DR: This paper investigates how it is possible to recover an automaton from a rational expression that has been computed from that automaton, and the notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem.
Abstract: In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.
Journal Article•
01 Jul 2004
TL;DR: A tableau-based algorithm for obtaining a Buchi automaton from a formula in dynamic linear time temporal logic (DLTL), a logic which extends LTL by indexing the until operator with regular programs.
Abstract: We present a tableau-based algorithm for obtaining a Buchi automaton from a formula in dynamic linear time temporal logic (DLTL), a logic which extends LTL by indexing the until operator with regular programs. The construction of the states of the automaton is similar to the standard construction for LTL, but a different technique must be used to verify the fulfillment of until formulas. The resulting automaton is a Buchi automaton rather than a generalized one. The construction can be done on-the-fly, while checking for the emptiness of the automaton.
TL;DR: The precision of right-hand context covering for conflict resolution is improved over previous NDR parsers, resulting in acceptation of wider subsets of LR-regular and LR-nonregular Grammars, including all LALR(k) grammars for a given k.
17 Aug 2004
TL;DR: In this article, the authors investigate the power of quantum pushdown automata whose stack is assumed to be implemented as a classical device, and show that they are strictly more powerful than classical counterparts in the one-sided error setting.
Abstract: One of important questions on quantum computing is whether there is a computational gap between the models that are allowed to use quantum effects and the models that are not. Several types of quantum computation models have been proposed, including quantum finite automata and quantum pushdown automata (with quantum pushdown stack). It has been shown that some quantum computation models are more powerful than classical counterparts and some are not since quantum computation models are required to obey some restrictions such as reversible state transitions. In this paper, we investigate the power of quantum pushdown automata whose stack is assumed to be implemented as a classical device, and show that they are strictly more powerful than classical counterparts in the one-sided error setting. That is, we show that there is a non-context-free language which quantum pushdown automata with classical stack operations can recognize with one-sided error.
Journal Article•
TL;DR: It is proved that there exists pushdown games, equipped with winning conditions in the form of Ω$_{A_1rA_2}$, where the winning sets are not deterministic context free languages, giving examples of winning sets which are non-deterministic non-ambiguous contextFree languages, inherently ambiguous contextfree languages, or even non context free Languages.
Abstract: In a recent paper [19, 20] Serre has presented some decidable winning conditions Ω$_{A_1rmrA_nrA_{n+1}}$ of arbitrarily high finite Borel complexity for games on finite graphs or on pushdown graphs. We answer in this paper several questions which were raised by Serre in [19,20]. We study classes C$_n$(A), defined in [20], and show that these classes are included in the class of non-ambiguous context free ω-languages. Moreover from the study of a larger class C$_n^λ$(A) we infer that the complements of languages in C$_n$(A) are also non-ambiguous context free ω-languages. We conclude the study of classes C$_n$(A) by showing that they are neither closed under union nor under intersection.We prove also that there exists pushdown games, equipped with winning conditions in the form Ω$_{A_1rA_2}$, where the winning sets are not deterministic context free languages, giving examples of winning sets which are non-deterministic non-ambiguous context free languages, inherently ambiguous context free languages, or even non context free languages.
01 Feb 2004
TL;DR: Team pushdown automata are introduced as a theoretical framework capable of modelling various communication and cooperation strategies in complex, distributed systems and their accepting capacity is studied.
Abstract: We introduce team pushdown automata as a theoretical framework capable of modelling various communication and cooperation strategies in complex, distributed systems. Team pushdown automata are obtained by augmenting distributed pushdown automata with the notion of team cooperation or — alternatively — by augmenting team automata with pushdown memory. Here we study their accepting capacity.